Load Data and Codes

Read dataset with id, site, period, species, abund

data <- read.csv("data.csv", h = T)
head(data)

##   ID Site Period                   species Nr
## 1  1   42      1            Noctua pronuba  8
## 2  2   42      1      Atlantarctia tigrina  1
## 3  3   42      1           Anarta myrtilli  1
## 4  4   42      1      Lycophotia molothina  7
## 5  5   42      1        Harpyia milhauseri  1
## 6  6   42      1 Pseudoterpna coronillaria  1

source('chao.R')
source('distanc.R')

Distances

The distances between pairs were calculated using QGIS for IPCC and IGeoE:

Hayford Gauss IPCC:

dist <- read.csv("dist_mat_ipcc.csv", h = T)
dist <- dist[-1]
DIST1 <- distanc(dist)
head(DIST1)

##      [,1] [,2]   [,3]
## [1,]    1    2  60.00
## [2,]    1    3  60.00
## [3,]    1    4  84.85
## [4,]    1    5 247.39
## [5,]    1    6 247.40
## [6,]    1    7 339.41

Hayford Gauss IGeoE

dist <- read.csv("dist_mat_igeoe.csv", h = T)
dist <- dist[-1]
DIST2 <- distanc(dist)
head(DIST2)

##      [,1] [,2]   [,3]
## [1,]    1    2  60.00
## [2,]    1    3  60.00
## [3,]    1    4  84.85
## [4,]    1    5 247.39
## [5,]    1    6 247.40
## [6,]    1    7 339.41

par(mfrow=c(2, 1))
hist(DIST1[, 3], main = "IPCC", xlab = "Geographic distance (m)", ylab = "Frequency")
hist(DIST2[, 3], main = "IGEOE", xlab = "Geographic distance (m)", ylab = "Frequency")

plot of chunk unnamed-chunk-4

The histograms have the same behavior, then I chose the first vector of distances (IPCC) for analysing the data.

Data

Sorensen and Jaccard Estimators were estimated using unseen species (Chao et al 2005). The data-set was subseted by sample. Variables created from the chao-function have the following columns:

sample1 <- chao(1, 1, "sample1")
sample2 <- chao(2, 2, "sample2")
sample3 <- chao(3, 3, "sample3")
sample4 <- chao(4, 4, "sample4")
sample5 <- chao(5, 5, "sample5")
sample6 <- chao(6, 6, "sample6")

p: sampling period.
s1: the code of sample 1.
s2: the code of sample 2.
n: the number of observed species in the sample 1.
nsp1: the number of species in the sample 1.
m: the number of observed species in the sample 2.
nsp2: the number of species in the sample 2.
nsh: the number of observed shared species in the two samples.
fm1: the observed number of shared species that occur once in sample 2.
fm2: the observed number of shared species that occur twice in sample 2.
f1m: the observed number of shared species that occur once in sample 1.
f2m: the observed number of shared species that occur twice in sample 1.
u_pt1: abundance sum of shared species divided by species number for the sample 1.
v_pt1: abundance sum of shared species divided by species number for the sample 2.
Junad: Jaccard unadjusted estimator.
Lunad: Sorensen unadjusted estimator.
U: u_pt1 plus unseen species for the sample 2.
V: v_pt1 plus unseen species for the sample 1.
Jabd: Jaccard adjusted estimator.
Labd: Sorensen adjusted estimator.

head(sample1)

##      p s1 s2  n nsp1   m nsp2 nsh fm1 fm2 f1m f2m   u_pt1  v_pt1  Junad
## [1,] 1  1  2 44   17  72   26  13   4   2   5   4 0.88636 0.6667 0.6142
## [2,] 1  1  3 44   17  73   33  13   5   1   5   5 0.86364 0.6301 0.5731
## [3,] 1  1  4 44   17   4    4   1   1   1   0   1 0.04545 0.2500 0.0400
## [4,] 1  1  5 44   17 114   33  12   2   1   4   4 0.86364 0.6754 0.6103
## [5,] 1  1  6 44   17  67   25  10   4   2   4   2 0.77273 0.4328 0.3840
## [6,] 1  1  7 44   17  97   29  12   3   1   5   4 0.81818 0.7216 0.6219
##        Lunad      U      V    Jabd   Labd
## [1,] 0.76098 1.0000 0.7854 0.78543 0.8798
## [2,] 0.72864 1.0000 0.7172 0.71715 0.8353
## [3,] 0.07692 0.0625 0.2500 0.05263 0.1000
## [4,] 0.75803 0.9312 0.7440 0.70526 0.8272
## [5,] 0.55487 1.0000 0.5495 0.54953 0.7093
## [6,] 0.76689 1.0000 0.9231 0.92315 0.9600

Exploratory Analysis

These functions were used to synthesize the samples for each year. Moth samplings were conducted for two years (2011 and 2012), each year had three sampling period.

trisamples <- function(base1, base2, base3, vr){
  base <- matrix(0, nrow = dim(base1)[1])
  for(i in 1:dim(base1)[1]){
    base[i] <- (base1[i, vr] + base2[i, vr] + base3[i, vr])/3
  }
  base
}

bisamples <- function(base1, base2){
  base <- matrix(0, nrow = length(base1))
  for(i in 1:length(base1)){
    base[i] <- (base1[i] + base2[i])/2
  }
  base
}

Calculated the dissimilarity average per site for first year

Jperiod1 <- trisamples(sample1, sample2, sample3, 19)
Lperiod1 <- trisamples(sample1, sample2, sample3, 20)

par(mfrow=c(1, 2))
plot(DIST1[, 3], (1 - Jperiod1), ylim = c(0, 1), xlab = "Geographic Distance (m)", ylab = expression(~beta*"-diversity"), main = "Jaccard")
plot(DIST1[, 3], (1 - Lperiod1), ylim = c(0, 1), xlab = "Geographic Distance (m)", ylab = expression(~beta*"-diversity"), main = "Sorensen")

plot of chunk unnamed-chunk-9

Calculated the dissimilarity average per site for second year

Jperiod2 <- trisamples(sample4, sample5, sample6, 19)
Lperiod2 <- trisamples(sample4, sample5, sample6, 20)

par(mfrow=c(1, 2))
plot(DIST1[, 3], (1 - Jperiod2), ylim = c(0, 1), xlab = "Geographic Distance (m)", ylab = expression(~beta*"-diversity"), main = "Jaccard")
plot(DIST1[, 3], (1 - Lperiod2), ylim = c(0, 1), xlab = "Geographic Distance (m)", ylab = expression(~beta*"-diversity"), main = "Sorensen")

plot of chunk unnamed-chunk-11 * Calculated the dissimilarity average per site for both years

Jperiod <- bisamples(Jperiod1, Jperiod2)
Lperiod <- bisamples(Lperiod1, Lperiod2)

par(mfrow=c(1, 2))
plot(DIST1[, 3], (1 - Jperiod), ylim = c(0, 1), xlab = "Geographic Distance (m)", ylab = expression(~beta*"-diversity"), main = "Jaccard")
plot(DIST1[, 3], (1 - Lperiod), ylim = c(0, 1), xlab = "Geographic Distance (m)", ylab = expression(~beta*"-diversity"), main = "Sorensen")

DATASET: I created a new database with six columns:

p: no functionality, I created just to standardize with other functions previously created.
s1: site 1
s2: site 2
Jabd: Jaccard adjusted estimator
Labd: Sorensen adjusted estimator
ipcc: distance between site 1 and site 2 (Hayford Gauss IPCC)

b.div.mean <- cbind(sample1[, 1], sample1[, 2], sample1[, 3], Jperiod, Lperiod, DIST1[, 3])
colnames(b.div.mean) <- c("p", "s1", "s2", "Jabd", "Labd", "ipcc")

head(b.div.mean)

##      p s1 s2   Jabd   Labd   ipcc
## [1,] 1  1  2 0.6520 0.7724  60.00
## [2,] 1  1  3 0.7169 0.8153  60.00
## [3,] 1  1  4 0.2347 0.3054  84.85
## [4,] 1  1  5 0.5494 0.6839 247.39
## [5,] 1  1  6 0.6330 0.7575 247.40
## [6,] 1  1  7 0.6073 0.7244 339.41

Samples were taken in three landscapes that represent the farmland abandonment gradient: meadow-dominated, shrub-dominated and forest-dominated. In each landscape had 28 fixed sampling sites divided into four biotopes (meadow, short shrub, tall shrub and woodland), totaling 84 sampling sites.

forest-dominated:

mf <- c(56) #m - meadow
sf <- c(36, 39, 42, 45, 46) #s - short shrub
tf <- c(34, 49) #t - tall shrub
wf <- c(29, 30, 31, 32, 33, 35, 37, 38, 40, 41, 43, 44, 47, 48, 50, 51, 52, 53, 54, 55) #w - woodland

shrub-dominated (m - mixed)

mm <- c(68, 75, 77, 84)
sm <- c(60, 64, 65, 66, 67, 70, 78, 79, 82)
tm <- c(57, 58, 59, 61, 62, 63, 69, 71, 72, 74, 76)
wm <- c(73, 80, 81, 83)

meadow-dominated (a - agriculture)

ma <- c(1, 9, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 27)
sa <- c(2, 8, 10, 11, 12, 13, 20)
ta <- c(3, 4, 5, 6, 7, 28)
wa <- c(22, 26)

within landscapes

landsc_within <- function(base, s1, s2){
  result <- NULL
  for(i in s1){
    for(j in s2){
      if(i != j){
        result <- rbind(result, base[base[, 2] == i & base[, 3] == j, ])
      }
    }
  }
  result
}

This function creates a database for each landscape. Also, I analyzed separately short and tall shrub within the shrub-dominated landscape.

In this analysis only the biotopes that correspond the type of the landscape were considered.

agr.mea <- landsc_within(b.div.mean, ma, ma)
shr.shr <- landsc_within(b.div.mean, sm, sm)
tal.shr <- landsc_within(b.div.mean, tm, tm)
for.woo <- landsc_within(b.div.mean, wf, wf)
mix.shr <- landsc_within(b.div.mean, c(sm, tm), c(sm, tm))

Regression models

Jaccard Estimator

jmodelfor.woo <- lm((1 - for.woo[, 4]) ~ for.woo[, 6])
jmodelmix.shr <- lm((1 - mix.shr[, 4]) ~ mix.shr[, 6])
jmodelagr.mea <- lm((1 - agr.mea[, 4]) ~ agr.mea[, 6])
jmodelshr.shr <- lm((1 - shr.shr[, 4]) ~ shr.shr[, 6])
jmodeltal.shr <- lm((1 - tal.shr[, 4]) ~ tal.shr[, 6])

Sorensen Estimator

smodelfor.woo <- lm((1 - for.woo[, 5]) ~ for.woo[, 6])
smodelmix.shr <- lm((1 - mix.shr[, 5]) ~ mix.shr[, 6])
smodelagr.mea <- lm((1 - agr.mea[, 5]) ~ agr.mea[, 6])
smodelshr.shr <- lm((1 - shr.shr[, 5]) ~ shr.shr[, 6])
smodeltal.shr <- lm((1 - tal.shr[, 5]) ~ tal.shr[, 6])

Short and tall shrubs are together in Shrub (right side: Jaccard and left side: Sorensen)
Short and tall shrubs are separated (right side: Jaccard and left side: Sorensen)
Mean Dissimilaritiy for each landscape (with standard deviations)

par(mfrow=c(1, 2))
m.data <- c(mean(for.woo[, 4]), mean(mix.shr[, 4]), mean(agr.mea[, 4]))
m.li <- c(mean(for.woo[, 4]) - sd(for.woo[, 4]), mean(mix.shr[, 4]) - sd(mix.shr[, 4]), mean(agr.mea[, 4]) - sd(agr.mea[, 4]))
m.lu <- c(mean(for.woo[, 4]) + sd(for.woo[, 4]), mean(mix.shr[, 4]) + sd(mix.shr[, 4]), mean(agr.mea[, 4]) + sd(agr.mea[, 4]))
plot(1:3, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Jaccard adjusted")
axis(1, at = 1:3, labels = c("Forest", "Shrub", "Meadow"))
segments(x0 = 1:3, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

m.data <- c( mean(for.woo[, 5]), mean(mix.shr[, 5]), mean(agr.mea[, 5]))
m.li <- c(mean(for.woo[, 5]) - sd(for.woo[, 5]), mean(mix.shr[, 5]) - sd(mix.shr[, 5]), mean(agr.mea[, 5]) - sd(agr.mea[, 5]))
m.lu <- c(mean(for.woo[, 5]) + sd(for.woo[, 5]), mean(mix.shr[, 5]) + sd(mix.shr[, 5]), mean(agr.mea[, 5]) + sd(agr.mea[, 5]))
plot(1:3, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Sorensen adjusted")
axis(1, at = 1:3, labels = c("Forest", "Shrub", "Meadow"))
segments(x0 = 1:3, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

plot of chunk unnamed-chunk-24

Mean Dissimilarity for each landscape (with tall and short shrub separately)

par(mfrow=c(1, 2))
m.data <- c(mean(for.woo[, 4]), mean(tal.shr[, 4]), mean(shr.shr[, 4]), mean(agr.mea[, 4]))
m.li <- c(mean(for.woo[, 4]) - sd(for.woo[, 4]), mean(tal.shr[, 4]) - sd(tal.shr[, 4]), mean(shr.shr[, 4]) - sd(shr.shr[, 4]), mean(agr.mea[, 4]) - sd(agr.mea[, 4]))
m.lu <- c(mean(for.woo[, 4]) + sd(for.woo[, 4]), mean(tal.shr[, 4]) + sd(tal.shr[, 4]), mean(shr.shr[, 4]) + sd(shr.shr[, 4]), mean(agr.mea[, 4]) + sd(agr.mea[, 4]))
plot(1:4, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Jaccard adjusted")
axis(1, at = 1:4, labels = c("Forest", "Tall", "Short", "Meadow"))
segments(x0 = 1:4, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

m.data <- c(mean(for.woo[, 5]), mean(tal.shr[, 5]), mean(shr.shr[, 5]), mean(agr.mea[, 5]))
m.li <- c(mean(for.woo[, 5]) - sd(for.woo[, 5]), mean(tal.shr[, 5]) - sd(tal.shr[, 5]), mean(shr.shr[, 5]) - sd(shr.shr[, 5]), mean(agr.mea[, 5]) - sd(agr.mea[, 5]))
m.lu <- c(mean(for.woo[, 5]) + sd(for.woo[, 5]), mean(tal.shr[, 5]) + sd(tal.shr[, 5]), mean(shr.shr[, 5]) + sd(shr.shr[, 5]), mean(agr.mea[, 5]) + sd(agr.mea[, 5]))
plot(1:4, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Sorensen adjusted")
axis(1, at = 1:4, labels = c("Forest", "Tall", "Short", "Meadow"))
segments(x0 = 1:4, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

plot of chunk unnamed-chunk-25

between landscapes

landsc_between <- function(base, s1, s2){
  result <- NULL
  for(i in s1){
    for(j in s2){
      result <- rbind(result, base[(base[, 2] == i & base[, 3] == j) | (base[, 2] == j & base[, 3] == i), ])
    }
  }
  result
}

This function creates a database of pairs of biotypes of the same type, but are in different landscapes. Also, I analyzed separately short and tall shrub among landscapes.

mea <- landsc_between(b.div.mean, ma, c(mm, mf))
shr <- landsc_between(b.div.mean, sm, c(sa, sf))
tal <- landsc_between(b.div.mean, tm, c(ta, tf))
woo <- landsc_between(b.div.mean, wf, c(wa, wm))
mix <- rbind(shr, tal)

Regreesion models

Jaccard Estimator

jmodelwoo <- lm((1 - woo[, 4]) ~ woo[, 6])
jmodelmix <- lm((1 - mix[, 4]) ~ mix[, 6])
jmodelmea <- lm((1 - mea[, 4]) ~ mea[, 6])
jmodelshr <- lm((1 - shr[, 4]) ~ shr[, 6])
jmodeltal <- lm((1 - tal[, 4]) ~ tal[, 6])

Sorensen Estimator

smodelwoo <- lm((1 - woo[, 5]) ~ woo[, 6])
smodelmix <- lm((1 - mix[, 5]) ~ mix[, 6])
smodelmea <- lm((1 - mea[, 5]) ~ mea[, 6])
smodelshr <- lm((1 - shr[, 5]) ~ shr[, 6])
smodeltal <- lm((1 - tal[, 5]) ~ tal[, 6])

Short and tall shrubs are together in Shrub (right side: Jaccard and left side: Sorensen)
Short and tall shrubs are separated (right side: Jaccard and left side: Sorensen)
Mean Dissimilarity for each landscape (with standard deviations)

par(mfrow=c(1, 2))
m.data <- c(mean(woo[, 4]), mean(mix[, 4]), mean(mea[, 4]) )
m.li <- c(mean(woo[, 4]) - sd(woo[, 4]), mean(mix[, 4]) - sd(mix[, 4]), mean(mea[, 4]) - sd(mea[, 4]))
m.lu <- c(mean(woo[, 4]) + sd(woo[, 4]), mean(mix[, 4]) + sd(mix[, 4]), mean(mea[, 4]) + sd(mea[, 4]))
plot(1:3, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Jaccard adjusted")
axis(1, at = 1:3, labels = c("Forest", "Shrub", "Meadow"))
segments(x0 = 1:3, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

m.data <- c(mean(woo[, 5]), mean(mix[, 5]), mean(mea[, 5]) )
m.li <- c(mean(woo[, 5]) - sd(woo[, 5]), mean(mix[, 5]) - sd(mix[, 5]), mean(mea[, 5]) - sd(mea[, 5]))
m.lu <- c(mean(woo[, 5]) + sd(woo[, 5]), mean(mix[, 5]) + sd(mix[, 5]), mean(mea[, 5]) + sd(mea[, 5]))
plot(1:3, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Sorensen adjusted")
axis(1, at = 1:3, labels = c("Forest", "Shrub", "Meadow"))
segments(x0 = 1:3, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

plot of chunk unnamed-chunk-32

Mean Dissimilarity for each landscape (with tall and short shrub separately)

par(mfrow=c(1, 2))
m.data <- c(mean(woo[, 4]), mean(tal[, 4]), mean(shr[, 4]), mean(mea[, 4]) )
m.li <- c(mean(woo[, 4]) - sd(woo[, 4]), mean(tal[, 4]) - sd(tal[, 4]), mean(shr[, 4]) - sd(shr[, 4]), mean(mea[, 4]) - sd(mea[, 4]))
m.lu <- c(mean(woo[, 4]) + sd(woo[, 4]), mean(tal[, 4]) + sd(tal[, 4]), mean(shr[, 4]) + sd(shr[, 4]), mean(mea[, 4]) + sd(mea[, 4]))
plot(1:4, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Jaccard adjusted")
axis(1, at = 1:4, labels = c("Forest", "Tall", "Short", "Meadow"))
segments(x0 = 1:4, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

m.data <- c(mean(woo[, 5]), mean(tal[, 5]), mean(shr[, 5]), mean(mea[, 5]) )
m.li <- c(mean(woo[, 5]) - sd(woo[, 5]), mean(tal[, 5]) - sd(tal[, 5]), mean(shr[, 5]) - sd(shr[, 5]), mean(mea[, 5]) - sd(mea[, 5]))
m.lu <- c(mean(woo[, 5]) + sd(woo[, 5]), mean(tal[, 5]) + sd(tal[, 5]), mean(shr[, 5]) + sd(shr[, 5]), mean(mea[, 5]) + sd(mea[, 5]))
plot(1:4, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Sorensen adjusted")
axis(1, at = 1:4, labels = c("Forest", "Tall", "Short", "Meadow"))
segments(x0 = 1:4, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

plot of chunk unnamed-chunk-33

Biotopes

mfma <- c(mf, mm, ma)
sfma <- c(sf, sm, sa)
tfma <- c(tf, tm, ta)
wfma <- c(wf, wm, wa)
mixf <- c(sf, sm, sa, tf, tm, ta)

This function creates databse for each biotope independent landscape.

mea.bio <- landsc_within(b.div.mean, mfma, mfma)
sho.bio <- landsc_within(b.div.mean, sfma, sfma)
tal.bio <- landsc_within(b.div.mean, tfma, tfma)
woo.bio <- landsc_within(b.div.mean, wfma, wfma)
mix.bio <- landsc_within(b.div.mean, mixf, mixf)

Regression models

Jaccard Estimator

jmodelwoo.bio <- lm((1 - woo.bio[, 4]) ~ woo.bio[, 6])
jmodelmix.bio <- lm((1 - mix.bio[, 4]) ~ mix.bio[, 6])
jmodelmea.bio <- lm((1 - mea.bio[, 4]) ~ mea.bio[, 6])
jmodelsho.bio <- lm((1 - sho.bio[, 4]) ~ sho.bio[, 6])
jmodeltal.bio <- lm((1 - tal.bio[, 4]) ~ tal.bio[, 6])

Sorensen Estimator

smodelwoo.bio <- lm((1 - woo.bio[, 5]) ~ woo.bio[, 6])
smodelmix.bio <- lm((1 - mix.bio[, 5]) ~ mix.bio[, 6])
smodelmea.bio <- lm((1 - mea.bio[, 5]) ~ mea.bio[, 6])
smodelsho.bio <- lm((1 - sho.bio[, 5]) ~ sho.bio[, 6])
smodeltal.bio <- lm((1 - tal.bio[, 5]) ~ tal.bio[, 6])

Short and tall shrubs are together (right side: Jaccard and left side: Sorensen)
Short and tall shrubs are separated (right side: Jaccard and left side: Sorensen)
Mean Dissimilarity for each landscape (with standard deviations)

par(mfrow=c(1, 2))
m.data <- c(mean(woo.bio[, 4]), mean(mix.bio[, 4]), mean(mea.bio[, 4]))
m.li <- c(mean(woo.bio[, 4]) - sd(woo.bio[, 4]), mean(mix.bio[, 4]) - sd(mix.bio[, 4]), mean(mea.bio[, 4]) - sd(mea.bio[, 4]))
m.lu <- c(mean(woo.bio[, 4]) + sd(woo.bio[, 4]), mean(mix.bio[, 4]) + sd(mix.bio[, 4]), mean(mea.bio[, 4]) + sd(mea.bio[, 4]))
plot(1:3, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Jaccard adjusted")
axis(1, at = 1:3, labels = c("Forest", "Shrub", "Meadow"))
segments(x0 = 1:3, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

m.data <- c( mean(woo.bio[, 5]), mean(mix.bio[, 5]), mean(mea.bio[, 5]))
m.li <- c(mean(woo.bio[, 5]) - sd(woo.bio[, 5]), mean(mix.bio[, 5]) - sd(mix.bio[, 5]), mean(mea.bio[, 5]) - sd(mea.bio[, 5]))
m.lu <- c(mean(woo.bio[, 5]) + sd(woo.bio[, 5]), mean(mix.bio[, 5]) + sd(mix.bio[, 5]), mean(mea.bio[, 5]) + sd(mea.bio[, 5]))
plot(1:3, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Sorensen adjusted")
axis(1, at = 1:3, labels = c("Forest", "Shrub", "Meadow"))
segments(x0 = 1:3, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

plot of chunk unnamed-chunk-40

Mean Dissimilarity for each landscape (with tall and short shrubs separately)

par(mfrow=c(1, 2))
m.data <- c(mean(woo.bio[, 4]), mean(tal.bio[, 4]), mean(sho.bio[, 4]), mean(mea.bio[, 4]))
m.li <- c(mean(woo.bio[, 4]) - sd(woo.bio[, 4]), mean(tal.bio[, 4]) - sd(tal.bio[, 4]), mean(sho.bio[, 4]) - sd(sho.bio[, 4]), mean(mea.bio[, 4]) - sd(mea.bio[, 4]))
m.lu <- c(mean(woo.bio[, 4]) + sd(woo.bio[, 4]), mean(tal.bio[, 4]) + sd(tal.bio[, 4]), mean(sho.bio[, 4]) + sd(sho.bio[, 4]), mean(mea.bio[, 4]) + sd(mea.bio[, 4]))
plot(1:4, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Jaccard adjusted")
axis(1, at = 1:4, labels = c("Forest", "Tall", "Short", "Meadow"))
segments(x0 = 1:4, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

m.data <- c(mean(woo.bio[, 5]), mean(tal.bio[, 5]), mean(sho.bio[, 5]), mean(mea.bio[, 5]))
m.li <- c(mean(woo.bio[, 5]) - sd(woo.bio[, 5]), mean(tal.bio[, 5]) - sd(tal.bio[, 5]), mean(sho.bio[, 5]) - sd(sho.bio[, 5]), mean(mea.bio[, 5]) - sd(mea.bio[, 5]))
m.lu <- c(mean(woo.bio[, 5]) + sd(woo.bio[, 5]), mean(tal.bio[, 5]) + sd(tal.bio[, 5]), mean(sho.bio[, 5]) + sd(sho.bio[, 5]), mean(mea.bio[, 5]) + sd(mea.bio[, 5]))
plot(1:4, 1 - m.data, xaxt = "n", ylim=c(0, 1), xlab = "", ylab = expression(~beta*"-diversity"), main = "Sorensen adjusted")
axis(1, at = 1:4, labels = c("Forest", "Tall", "Short", "Meadow"))
segments(x0 = 1:4, y0 = 1 - m.li, y1 = 1 - m.lu, col = 1)

plot of chunk unnamed-chunk-41

Mean Dissimilarity for each scale
Mean Dissimilarity for each scale (with tall and short shrubs separately) —

Bootstrapping

library(boot)
# function to obtain regression weights 
bs.jac <- function(formula, data, ind){
  d <- data[ind,] # allows boot to select sample
  fit <- lm(formula, data = d)
  return(c(coef(fit), summary(fit)$r.square, mean(d[, 4]))) 
} 

bs.sor <- function(formula, data, ind){
  d <- data[ind,] # allows boot to select sample
  fit <- lm(formula, data = d)
  return(c(coef(fit), summary(fit)$r.square, mean(d[, 5]))) 
}

Within Landscape

# bootstrapping with 2000 replications
wl.jforres <- boot(data = as.data.frame(for.woo), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
wl.sforres <- boot(data = as.data.frame(for.woo), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

wl.jmixres <- boot(data = as.data.frame(mix.shr), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
wl.smixres <- boot(data = as.data.frame(mix.shr), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

wl.jtalres <- boot(data = as.data.frame(tal.shr), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
wl.stalres <- boot(data = as.data.frame(tal.shr), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

wl.jshrres <- boot(data = as.data.frame(shr.shr), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
wl.sshrres <- boot(data = as.data.frame(shr.shr), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

wl.jmeares <- boot(data = as.data.frame(agr.mea), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
wl.smeares <- boot(data = as.data.frame(agr.mea), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

Between Landscapes

# bootstrapping with 2000 replications
bl.jwoores <- boot(data = as.data.frame(woo), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
bl.swoores <- boot(data = as.data.frame(woo), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

bl.jmixres <- boot(data = as.data.frame(mix), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
bl.smixres <- boot(data = as.data.frame(mix), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

bl.jtalres <- boot(data = as.data.frame(tal), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
bl.stalres <- boot(data = as.data.frame(tal), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

bl.jshrres <- boot(data = as.data.frame(shr), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
bl.sshrres <- boot(data = as.data.frame(shr), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

bl.jmeares <- boot(data = as.data.frame(mea), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
bl.smeares <- boot(data = as.data.frame(mea), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

All Biotopes

# bootstrapping with 2000 replications
al.jforres <- boot(data = as.data.frame(woo.bio), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
al.sforres <- boot(data = as.data.frame(woo.bio), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

al.jmixres <- boot(data = as.data.frame(mix.bio), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
al.smixres <- boot(data = as.data.frame(mix.bio), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

al.jtalres <- boot(data = as.data.frame(tal.bio), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
al.stalres <- boot(data = as.data.frame(tal.bio), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

al.jshrres <- boot(data = as.data.frame(sho.bio), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
al.sshrres <- boot(data = as.data.frame(sho.bio), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

al.jmeares <- boot(data = as.data.frame(mea.bio), statistic = bs.jac, R = 2000, formula = (1 - Jabd) ~ ipcc)
al.smeares <- boot(data = as.data.frame(mea.bio), statistic = bs.sor, R = 2000, formula = (1 - Labd) ~ ipcc)

Confidence Interval

Within Landscape - get 95% confidence intervals

Jaccard Estimator

wl.jforres.ci <- ci.boot(wl.jforres)
wl.jmixres.ci <- ci.boot(wl.jmixres)
wl.jtalres.ci <- ci.boot(wl.jtalres)
wl.jshrres.ci <- ci.boot(wl.jshrres)

## Warning: extreme order statistics used as endpoints

wl.jmeares.ci <- ci.boot(wl.jmeares)

Sorensen Estimator

wl.sforres.ci <- ci.boot(wl.sforres)
wl.smixres.ci <- ci.boot(wl.smixres)
wl.stalres.ci <- ci.boot(wl.stalres)
wl.sshrres.ci <- ci.boot(wl.sshrres)
wl.smeares.ci <- ci.boot(wl.smeares)

Between Landscapes - get 95% confidence intervals

Jaccard Estimator

bl.jforres.ci <- ci.boot(bl.jwoores)
bl.jmixres.ci <- ci.boot(bl.jmixres)
bl.jtalres.ci <- ci.boot(bl.jtalres)
bl.jshrres.ci <- ci.boot(bl.jshrres)
bl.jmeares.ci <- ci.boot(bl.jmeares)

Sorensen Estimator

bl.sforres.ci <- ci.boot(bl.swoores)
bl.smixres.ci <- ci.boot(bl.smixres)
bl.stalres.ci <- ci.boot(bl.stalres)
bl.sshrres.ci <- ci.boot(bl.sshrres)
bl.smeares.ci <- ci.boot(bl.smeares)

All Biotopes - get 95% confidence intervals

Jaccard Estimator

al.jforres.ci <- ci.boot(al.jforres)
al.jmixres.ci <- ci.boot(al.jmixres)
al.jtalres.ci <- ci.boot(al.jtalres)
al.jshrres.ci <- ci.boot(al.jshrres)
al.jmeares.ci <- ci.boot(al.jmeares)

Sorensen Estimator

al.sforres.ci <- ci.boot(al.sforres)
al.smixres.ci <- ci.boot(al.smixres)
al.stalres.ci <- ci.boot(al.stalres)
al.sshrres.ci <- ci.boot(al.sshrres)
al.smeares.ci <- ci.boot(al.smeares)

Results 1

Jaccard

Intercept

par(mfrow = c(1, 3))
interc.plot3(wl.jforres.ci, wl.jmixres.ci, wl.jmeares.ci)
title("Within Landscape", cex = 1.5)
interc.plot3(bl.jforres.ci, bl.jmixres.ci, bl.jmeares.ci)
title("Between Landscapes", cex = 1.5)
interc.plot3(al.jforres.ci, al.jmixres.ci, al.jmeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-56

Dissimilarity

par(mfrow = c(1, 3))
dissim.plot3(wl.jforres.ci, wl.jmixres.ci, wl.jmeares.ci)
title("Within Landscape", cex = 1.5)
dissim.plot3(bl.jforres.ci, bl.jmixres.ci, bl.jmeares.ci)
title("Between Landscapes", cex = 1.5)
dissim.plot3(al.jforres.ci, al.jmixres.ci, al.jmeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-57

Slope

par(mfrow = c(1, 3))
slope.plot3(wl.jforres.ci, wl.jmixres.ci, wl.jmeares.ci)
title("Within Landscape", cex = 1.5)
slope.plot3(bl.jforres.ci, bl.jmixres.ci, bl.jmeares.ci)
title("Between Landscapes", cex = 1.5)
slope.plot3(al.jforres.ci, al.jmixres.ci, al.jmeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-58

R-Square

par(mfrow = c(1, 3))
rsquar.plot3(wl.jforres.ci, wl.jmixres.ci, wl.jmeares.ci)
title("Within Landscape", cex = 1.5)
rsquar.plot3(bl.jforres.ci, bl.jmixres.ci, bl.jmeares.ci)
title("Between Landscapes", cex = 1.5)
rsquar.plot3(al.jforres.ci, al.jmixres.ci, al.jmeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-59

Sorensen

Intercept

par(mfrow = c(1, 3))
interc.plot3(wl.sforres.ci, wl.smixres.ci, wl.smeares.ci)
title("Within Landscape", cex = 1.5)
interc.plot3(bl.sforres.ci, bl.smixres.ci, bl.smeares.ci)
title("Between Landscapes", cex = 1.5)
interc.plot3(al.sforres.ci, al.smixres.ci, al.smeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-60

Dissimilarity

par(mfrow = c(1, 3))
dissim.plot3(wl.sforres.ci, wl.smixres.ci, wl.smeares.ci)
title("Within Landscape", cex = 1.5)
dissim.plot3(bl.sforres.ci, bl.smixres.ci, bl.smeares.ci)
title("Between Landscapes", cex = 1.5)
dissim.plot3(al.sforres.ci, al.smixres.ci, al.smeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-61

Slope

par(mfrow = c(1, 3))
slope.plot3(wl.sforres.ci, wl.smixres.ci, wl.smeares.ci)
title("Within Landscape", cex = 1.5)
slope.plot3(bl.sforres.ci, bl.smixres.ci, bl.smeares.ci)
title("Between Landscapes", cex = 1.5)
slope.plot3(al.sforres.ci, al.smixres.ci, al.smeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-62

R-Square

par(mfrow = c(1, 3))
rsquar.plot3(wl.sforres.ci, wl.smixres.ci, wl.smeares.ci)
title("Within Landscape", cex = 1.5)
rsquar.plot3(bl.sforres.ci, bl.smixres.ci, bl.smeares.ci)
title("Between Landscapes", cex = 1.5)
rsquar.plot3(al.sforres.ci, al.smixres.ci, al.smeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-63

Results 2

Jaccard * Intercept

par(mfrow = c(1, 3))
interc.plot4(wl.jforres.ci, wl.jtalres.ci, wl.jshrres.ci, wl.jmeares.ci)
title("Within Landscape", cex = 1.5)
interc.plot4(bl.jforres.ci, wl.jtalres.ci, wl.jshrres.ci, bl.jmeares.ci)
title("Between Landscapes", cex = 1.5)
interc.plot4(al.jforres.ci, al.jtalres.ci, al.jshrres.ci, al.jmeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-64

Dissimilarity

par(mfrow = c(1, 3))
dissim.plot4(wl.jforres.ci, wl.jtalres.ci, wl.jshrres.ci, wl.jmeares.ci)
title("Within Landscape", cex = 1.5)
dissim.plot4(bl.jforres.ci, wl.jtalres.ci, wl.jshrres.ci, bl.jmeares.ci)
title("Between Landscapes", cex = 1.5)
dissim.plot4(al.jforres.ci, al.jtalres.ci, al.jshrres.ci, al.jmeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-65

Slope

par(mfrow = c(1, 3))
slope.plot4(wl.jforres.ci, wl.jtalres.ci, wl.jshrres.ci, wl.jmeares.ci)
title("Within Landscape", cex = 1.5)
slope.plot4(bl.jforres.ci, wl.jtalres.ci, wl.jshrres.ci, bl.jmeares.ci)
title("Between Landscapes", cex = 1.5)
slope.plot4(al.jforres.ci, al.jtalres.ci, al.jshrres.ci, al.jmeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-66

R-Square

par(mfrow = c(1, 3))
rsquar.plot4(wl.jforres.ci, wl.jtalres.ci, wl.jshrres.ci, wl.jmeares.ci)
title("Within Landscape", cex = 1.5)
rsquar.plot4(bl.jforres.ci, wl.jtalres.ci, wl.jshrres.ci, bl.jmeares.ci)
title("Between Landscapes", cex = 1.5)
rsquar.plot4(al.jforres.ci, al.jtalres.ci, al.jshrres.ci, al.jmeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-67

Sorensen

Intercept

par(mfrow = c(1, 3))
interc.plot4(wl.sforres.ci, wl.stalres.ci, wl.sshrres.ci, wl.smeares.ci)
title("Within Landscape", cex = 1.5)
interc.plot4(bl.sforres.ci, wl.stalres.ci, wl.sshrres.ci, bl.smeares.ci)
title("Between Landscapes", cex = 1.5)
interc.plot4(al.sforres.ci, al.stalres.ci, al.sshrres.ci, al.smeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-68

Dissimilarity

par(mfrow = c(1, 3))
dissim.plot4(wl.sforres.ci, wl.stalres.ci, wl.sshrres.ci, wl.smeares.ci)
title("Within Landscape", cex = 1.5)
dissim.plot4(bl.sforres.ci, wl.stalres.ci, wl.sshrres.ci, bl.smeares.ci)
title("Between Landscapes", cex = 1.5)
dissim.plot4(al.sforres.ci, al.stalres.ci, al.sshrres.ci, al.smeares.ci)

plot of chunk unnamed-chunk-69

Slope

par(mfrow = c(1, 3))
slope.plot4(wl.sforres.ci, wl.stalres.ci, wl.sshrres.ci, wl.smeares.ci)
title("Within Landscape", cex = 1.5)
slope.plot4(bl.sforres.ci, wl.stalres.ci, wl.sshrres.ci, bl.smeares.ci)
title("Between Landscapes", cex = 1.5)
slope.plot4(al.sforres.ci, al.stalres.ci, al.sshrres.ci, al.smeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-70

R-Square

par(mfrow = c(1, 3))
rsquar.plot4(wl.sforres.ci, wl.stalres.ci, wl.sshrres.ci, wl.smeares.ci)
title("Within Landscape", cex = 1.5)
rsquar.plot4(bl.sforres.ci, wl.stalres.ci, wl.sshrres.ci, bl.smeares.ci)
title("Between Landscapes", cex = 1.5)
rsquar.plot4(al.sforres.ci, al.stalres.ci, al.sshrres.ci, al.smeares.ci)
title("All Biotopes", cex = 1.5)

plot of chunk unnamed-chunk-71

Moth

Murilo Miranda

9 Sep 2014

Load Data and Codes

Distances

Data

Exploratory Analysis

Bootstrapping

Results 1

Results 2